Adjustable electrical phaseshifting network



Dec. 30, 1952 E. R. WlGAN 2,623,945

ADJUSTABLE ELECTRICAL PHASE-SHIFTING NETWORK Filed May 9, 1946 2SHEETS-SHEET l F/Gl. F/G.2. 5 6 s 6 1 lNVENTOR Z: 4 IpMdn/P KAMSAY Dec.30, 1952 E. R. WlGAN 2,623,945

ADJUSTABLE ELECTRICAL PHASE-SHIFTING NETWORK Filed May 9, 1946 2SI-IEETS-SHEET 2 Y F/ G. 5. W Y

CURVEa r, ZERO b SMALL mu: fb c r, GRIT/CA4 mus d r ZARGE VALUE F/G. 6

Q? 3 fa 2 to i 3 3 g z E m g g "R N E 1 Q X o s P x 0 05, K v H /N l/E NTOR Eunwvp EMMY Nisan ATTORNEY Patented Dec. 30, 1952 UNITED STATES T()FFICE ADJUSTABLE ELECTRICAL PHASE- SHIFTING NETWORK of DelawareApplication May 9, 1946, Serial No. 668,610 In Great Britain January 9,1945 Section 1, Public Law 690, August 8,1946 Patent expires January 9,1965 6 Claims.

The present invention relates to electrical" phaseshifting networks,with particular reference to networks which may be conveniently ad- 1.iusted'to produce a zero phase shift at any desired frequency ina-given range of frequencies.

The invention is of particular advantage when applied to the frequencydetermining network of an oscillator of 'the resistance-reactahce type,which includes a coupling network of the L type, having a series arm anda'shunt arm both of which include resistive and reactive elements, thefrequency of oscillation being substantially that for which the phaseshift'producecl by the net work is zero. Such .a. network may also beused in frequency meters.

As will be explained more fully later, in the present invention anadjustable impedance element is added to the conventional L network oithe resistance-reactance type, .andby means of this adjustable element,the frequency of zero phase shift may be varied over a certain range,while the network may also be designed so that the voltage transferratio of the network at the frequency of zero phase shift is independentof the frequency, and is determined by the series and shunt arms of "the:network. This is a valuable property of the invention because itenables the frequency of an oscillator to be varied without varying theoutput level, and, further if the adjustable impedance element beadapted to be varied in some way under the control of a signal forexample, if the element should be a microphone) substantially purefrequency modulation unaccompanied by amplitude modulation will beobtained in a very simple manner.

The invention accordingly provides an electrical phase shifting networkincluding resistive and reactive impedance elements arranged in seriesand shunt arms of the network, and comprising an additional impedanceelement connecting a point in a series arm with a point in a shunt arm,

the arrangement being such that the phase shift produced by the networkis zero at a frequency which depends on the magnitude of the additionalelement.

The invention will be described with reference to the accompanyingdrawings, in which:

Fig. -1 shows a schematic circuit diagram of a known type of phaseshifting network;

Fig. 2 shows the network of Fig. 1 modified according to the invention,to give one example illustrating the invention;

Fig. 8 shows a block schematic diagram of the most general networkaccording to the invention; r

, Fig. 4 shows a schematic circuit diagram which includes a group ofnetworks according to the invention;

Figs. 5 and-6 show characteristic curves of networks according to theinvention;

of particular networks according to the invention;

Fig. 11 shows a schematic circuit diagram of an oscillator incorporatinga network according to the invention; and

Figs. 12 and 13 show modifications of the networks of Fig. 2.

Fig. 1 shows a coupling network of well'known type often employed in aresistance-reactance type of oscillator. The input terminals I, 2 areconnected to the output terminals 3, 4 by a series arm including acondenser 5 in series with a re-- sistance 6, and a shunt arm includinga condenser l' in parallel with a resistance -8. Fig. 2 shows oneparticular example of a network according to the present invention, andis the same as Fig. 1 with the addition "of a resistance 9 (which may bevariable) connecting a point in the resistance 6 with a point in theresistance 8. It can be shown that by proper proportioning of theelements of the network, the phase shift beween the terminals l, 2 andthe terminals 3, s can be made zero at a particular frequency, andmoreover, if the resistance '9 be made'adjustable, the frequency of zerophase shift may be varied over a certain range. In addition, theelements of the network may be so designed that the voltage transferratio, that is, the'ratio of the output voltage to the input voltage, atthe frequency of zero phase shift, is constant.

Fig. 2 is, however, only one possible form of the network according tothe invention, which is indicated more generally in Fig. '3. The seriesarm includes two series impedances represented by blocks I8 and H, andthe shunt arm includes two impedances l2 and F3 connected in series, andshunted by another impedance It, still another impedance i5 beingconnected in series with the combination of l2, l3 and M. The adjustableimpedance It, which is the principal characteristic of the invention, isconnected between the junction points of impedances ill and l I andimpedance l2 and i3.

some of the blocks in to 15 may include both resistance and reac-tanceelements; and the series and shunt arms of the network must each of theminclude at least one resistance element and at least one 'reactaneeelement. The impedance Hi can be either a variable resistance or avariable reactance. The impedance I is not an essential element and maybe omitted, but when used will generally be a resistance element. Itwill be understood, of course, that reactance elements may be condensersor inductances. Usually, also, the impedances ll, 12, I3 and I 6 will beall of the same kind, that is, they will be all resistances, or a lreactances of the same sign.

It will be understood, also, that the networks included in Fig. 3 cangenerally be replaced by equivalent networks with the elements arrangedin other Ways, according to well known principles.

The elements of the network of Fig. 3 may be designed to fulfil desiredconditions by solution of the network according to well knownprinciples, but the general solution is involved and tedious, andaccordingly the solution in one or two typical cases will be quoted. Itis always assumed that the impedance to which the terminals 3 and i areconnected is substantially infinite.

In the particular case of Fig. 3 shown in Fig. 4, A

the impedance [9 consists of an element of reactance X1 in series with aresistance 1:. The

impedance Hi consists of an element of reaotance X2 in series with aresistance m. The impedances ll, [2, l3, l5 and it are resistances y, a,b, 1'1 and P respectively. It will be understood that the reactances X1and X2 may be represented either by condensers or by inductances.

The following additional symbols will be used:

K: (P+a+y) /(a+y) Voltage transfer ratio e2/e1=L;

It follows that BM ==d It will be first assumed that r2=0 Then it can beshown that the condition for zero phase shift is In practice it isusually desirable to be able to choose the value of the voltage transferratio L. It can be shown that at the frequency of zero phase shift, andwhen the network elements have been chosen so that L is the same at allsuch zero-phase-shift frequencies,

Equation 1 may then be written in a slightly different form usingEquation 2 The frequency of zero phase shift may be determined fromEquation 1 or 3 since it occurs in the reactances X1 and X2. For exampif f 4 is this frequency and if X1 and X2 are represented by condensersof capacities C1 and C2 then If X1 and X2 are represented by inductancesL1 and L2, then X1X2=4=1r f L1La It will be noted from Equation 1 thatwhen P is infinite, then the corresponding limiting value of thezero-phase-shift frequency is that frequency for which When P is zerothe corresponding limiting value of the zero-phase-shift frequency isthat fre quency for which From Equation 3, since K =1 when P=0.

Equation 7 indicates that when X1 and X2 are negative reactances, 11 maybe chosen so that the limiting zero-phase-shift frequency is infinitewhen P=0. Likewise when X1 and X2 are positive reactances 1'1 may bechosen so that the limiting zero-phase-shift frequency is zero when P=O.In both cases, of course, X1X2 is zero.

It is not practicable to give any very definite directions as to thechoice of values for the elements of the network to fulfil specifiedconditions, because the possibilities of choice are rather wide and theprocedure will often be determined by such factors as the limitationsset by the design or availability of certain of the elements. However,the process may be somewhat as follows:

When designing a network to cover a certain frequency range the firststep is to choose a value of L which is suitable for the circuitassociated with the network; for example, when the network is used in anoscillator, the value of L will be determined at least in part by thegain of the associated amplifier.

The parameters M, N and A are then chosen to satisfy Equation 2. Unlessa wide range of variation of the zero-phase-shift frequency byadjustment of P is required, A may be made zero by making r1 zero. Thetapping points to which the resistance P are to be connected aredetermined from Equation 4 or 5 from which d is found, and therefore Bmay be determined, since M has been already fixed.

Any value of 20 may now be selected, and from the value of B justdetermined the corresponding value of q is found. If a wide range ofvariation of the zero-phase-shift frequency is desired, a large value ofp should be chosen. All the quantities in Equation 1 are now fixedexcept the individual values of XiXzRi and R2. v

Let it be assumed that X1 and X2 are produced by condensers C1 and C2.Then the lowest frequency of the range will be obtained for the maximumpracticable value of P, and the highest frequency when P==0. A trialchoice of values of R1, B2, C1 and C2 should be made on the assumptionthat P is disconnected, in order to obtain the lowest desiredzero-phase-shift frequency. If R2 can conveniently be given a valuesmall compared with the highest practicable value of P, then this lowestfrequency will not be much affected when P is connected and set to itsmaximum value. A suitable value of ye may now be found from Equation 1in order to obtain the highest desired zero-phase-shift frequency when Phas its smallest practicable value. Then q is 5 determined from thevalue of B as already mentioned.

The manner in which the performance of the network of Fig. 4 (in whichthe reactances X1 and X2 are represented by condensers) depends on thevalue of the resistance 11 is shown in Fig. 5, in which thezero-phase-shiit frequency f is plotted against the value of P. Thecurve (or) represents the case when r1=0, and is asymptotic to a line QRparallel to OK, which line cuts the axis OY at the point Q representingthe minimum value of 1 when P is infinite. The curve (a) cuts the axisOY at a point corresponding t th i.. mum zero-phase-shift frequency fawhen P 0. When 11 has a small value, the corresponding curve (b) liesabove the curve (a) and cuts the axis OY at a point corresponding to ahigher maximum frequency fb.

The curve represents the special critical case when the value of n hasbeen chosen so that f is infinite when P is zero. This curve isasymptotic to OY.

The curve ((1) shows the case when n has a value larger than thecritical value. This curve is asymptotic to a line ST parallel to CY andcutting the axis OX in a point S corresponding to the minimum value of Pfor which any zero-phaseshift'frequency is possible.

It will be evident from Equation 6 that each of the curves (at), (b),(c), (at) will be asymptotic to a different line parallel to OK. Onlythe line QR corresponding to curve (a) has been shown, in order to avoidconfusing the figure.

It should be pointed out that the degree of separation of the curves(a), (b), (c), (at) depends on the value of p which has been selected.When a relatively large value of p is chosen, the curves are wellseparated, as shown in Fig. but for smaller values, the curves (b), (c)and (d) tend to move closer together, and to curve (a), and as papproaches zero they will all tend to coincide with curve (a) The curvesof Fig. 5 also represent the case in which the reactances X1 and X2 areprovided by inductances, so long as the scale of ordinates along OY isin terms of 1/ instead of in terms of 1.

When all the elements of the network have been selected, the Equation 3may be written in the form (b) f =AzA4/K where A1A2As and A4 areconstants, the forms (a) and (1)) corresponding respectively to thecases in which the reactances X1 and X2 are provided by condensers andinductances.

Equations 8 show in the simplest form the relation between P (which iscontained in K) and the corresponding zero-phase-shift frequency.

Fig. 6 shows 1/) for Equation 8(a) (or f for Equation 8(1)) plottedagainst 1/3 for the case in which 1' is larger than the critical value(curve ((5.), Fig. 5). The curve is a straight line cutting the axis ()Xand OY in V and W such that OW:A1(or A3) and the tangent of the angleOVW is A2 (or A1,). The value 0V or" l/K for infinite (or zero)zero-phase-shiit frequency is less than 1, so that F has a minimum valuecorresponding to OS in Fig. i" If the critical value of 1-1 is chosen(curve (c), Fig. 5), then the point V in Fig. 6 will be such that OVzl,and the whole of the range of P can then be used. This con- Equations 4and 5 remain unchanged.

In this case the various parameters may be chosen in a manner similar tothat explained above.

The equations corresponding to Equations 6 I for the limitingzero-phase-shift frequency when P is infinite are It will be understoodthat although for convenience the cases in which 11:0 and r2:0 have beentreated separately, networks may be used in which neither 1'1 nor T2 iszero.

It has already been pointed out that the reactances X1 and X2 of Fig. 4may be positive or negative. Another series of networks according to theinvention may be obtained by replacing the reactances X1 and X2 byresistances and the resistances 31, y, a, b and P by reactances all ofthe same kind.

Fig. 7 shows a typical example of one of these networks usingcapacitative reactances. The series arm of the network comprises aresistance ll connected in series with two condensers it and it, and theshunt arm comprises a resistance 26 in parallel with two seriesconnected condensers 2i and 22. A variable condenser 23 is connectedbetween the junction point of the condensers i3 and i9 and the junctionpoint of the condensers 2i and 22.

A resistance T1 (not shown) could be connected in series with the wholeof the shunt arm (in the manner shown in Fig. 4) if the performanceindicated by curve (b), (c) or (d) of Fig. 5 is required. Alternativelya condenser (not shown) having a reactance D times the reactance of thecondensers 2i and Z2 taken in series, may be connected in series withthe resistance 2% to give the performance just referred to, or both theresistance and the condenser may be provided.

For the network of Fig. '7, Equation 1 will be modified as follows:

Equation 4 is changed as follows;

l/L:1+BN-{M/(1+EN) (14) Equation 2 will be unchanged.

8 shows another circuit according to the invention, which can be shownby well known network transforming methods to be identically equivalentto the circuit of Fig. '2. It'will be noted that Fig. '8 differs fromFig. 2 in that the upper end of the shunt resistance 8 is connected tothe opposite end of the series resistance '6. If the capacities ofcondensers 5 and 'l in Fig. 8 are respectively equal to the capacitiesof condensers 7 and 5 in Fig. 2, then both networks have the samerelation between the value of P and the cero phas'e-shi'ft frequency,but the value of L is different unless the capacities of condensers 5and 1 are equal in each network. All the networks covered by 4 can betransformed in a similar way.

It may be pointed out that the networks including condensers aresuitable for high frequencies. Then there is always a finite lower limitto the zero-phase-shift frequency, but the upper limit, which occurswhen P approaches zero, can be made infinite if suitably proportionedresistances r1 and/r m be included. Likewise those including inductancesare more suitable for low frequencies. Then there is always a finiteupper limit to the zero-phase-shift frequency, but the lower limit,which occurs when P approaches zero, can be made zero by means of theresistances 7'1 and/or r2.

It should be noted, also, that the zero-phaseshift frequency can beadjusted in an alternative manner, namely by keeping P fixed andsimultaneously varying the tapping points on the series and shunt armsof the networks in such manner that p and q fulfil the conditions ofEquation 4 or or 14.

This is quite a practical scheme when the ele- As it may be inconvenientto divide the series 3' and shunt impedance elements of the network inorder to obtain the tapping points for the adjustable element P, thesame result may be achieved in a difierent way, an example or which isshown in Fig. 9 which is a modication of Fig. '7. In Fig. 9 thecondenser 24 replaces the two condensers I 8 and IQ of Fig. 7, and isshunted by two other condensers 25 and 26 connected in series. Likewisethe condenser 21 replaces the two condensers 2| and 22 of Fig. 7 and isshunted by the two condensers 2B and 29 connected in series. Thecondenser 23, which represents the variable element P, is connectedbetween the junction points of the condensers 25 and 25 and of thecondensers 28 and 29 respectively. The capacities of the condensers 24,25 and 26 will be chosen so that if the deltas 24, 25, 26 and 21, 23, 29be supposed replaced by the equivalent '1 arrangements, the capacitiesof the T which act effectively in series with the resistance I! arerespectively equal to the capacities of condensers l8 and I9 of Fig. '7.Similarly the effective series capacities of the T network equivalent tothe delta 21, 28, 29 should be respectively equal to the capacities ofthe two condensers 2| and 22.

The arrangement then operates in the same way as that of Fig. '7, exceptthat an additional reactance contributed by the shunt arms of theequivalent T networks acts effectively in series with the variableelement 23, so that this additional reactance must be included in thevalue of P, and sets a limit to its minimum value.

A similar delta arrangement can evidently be used in a network similarto Fig. 2 in which each of the resistances 6 and 8 could be shunted by atapped resistance, the resistance 9 being connected between the twotaps. The values of the resistances would be chosen according to thesame principles as in Fig. 9. Clearly, also an arrangement similar toFig. 9 could be used in which all the condensers are replaced byinductances.

It is evident also, that the delta arrangement could be used, ifdesired, for only one of the arms of the network.

This delta arrangement may be found convenient in order to avoid tappinga precision element. Thus in Fig. 9, the condensers 24 and 27 may behigh grade adjustable condensers in order to provide a number ofdifferent frequency ranges. In such a case tapping these condenserswould be impracticable, and the additional condensers such as 25 and 26can conveniently be provided with the proper capacity ratio, and wouldnot need to be changed when the condenser 24 is changed. This device isalso useful in other circumstances, an example of which occurs in Fig.12.

Referring again to Fig. 3, the introduction of the impedance [5 may betreated in a slightly different manner. Suppose that the elements ll] toM and 16 have been designed accordin to the principles already explainedso that a constant voltage transfer ratio at the zero-phase-shiftfrequency, determined by the adjustment of element [6, has beenobtained. Then for given setting of this element, the network isequivalent to the portion inside the dotted outline of Fig. 10, whichconsists of a series impedance Z1 and a shunt impedance Z2 whose valuescan be calculated according to well known principles from the values ofthe elements in to M and It. The voltage transfer ratio L will be Zz/(Z1+Z2) which, as already stated, will be constant at thezerophase-shift frequency for adjustments of the element l 6. If now theelement l 5 of impedance Z4 be introduced in series with Z2, then thevoltage transfer ratio of the whole network of Fig. 10 will still beequal to L provided with an impedance Z3 is introduced in series withZ1, as shown, having the valu (l-L)Z4/L. The relation between the valueof P and the zero-phase-shift frequency will be unchanged. It will beunderstood that Z3 and Z4 can be any type of impedances whatever,provided that their ratio is =(l- L) /L independent of frequency. Thus,for example, if Z4 comprises an inductance L0 in parallel with a seriescombination of a condenser of capacity Co and a resistance R0, thenimpedance Z3 will be an inductance ,uLo in parallel with a seriescombination of a condenser of capacity C/ and a resistance ,uRo. It isevident that Z3 and Z4 could comprise single impedance elements of anytype, or any kind of network of such elements.

It will be understood that the impedances Z3 and Z4 may be introduced inthis manner whether or not 7'2 is included in the shunt arm or" theoriginal network, and whatever be the form of the original network. Thevalue of L to be used is in all cases that of the original networkbefore Z3 and Z4 have been introduced.

When, as in the case first treated above, the impedance Z4 is aresistance T1 and when no corresponding impedanee Z3 is included in the.series arm, thenthe relation between P and the zerophase-shift frequencyis affected by T1, according to Equations 1 and 3 and the curves shownin Fig. 0.

in order further to illustrate the invention, some particular cases willbe quoted. A simple case of Fig. 2 is that for which.

From Equation 2 it follows that L=%;. If q 13 chosen equal to zero, sothat the variable re- 9. sistance P is connected to the junction point Cand R in the series arm, then it follows from Equation 4 or thatp=0.618.

It can be shown from Equation 1 by putting P=0 and P= therein, that theratio of the maximum to the minimum zero-phase-shiftfrequency is 2.618.

P (ohms) f (O./S.)

This simple case gives a rather small total variation of thezero-phase-shift frequency, and as already explained, the introductionof a suitable resistance 11 will enable this range to be extended toinfinity. A suitable value of H can be obtained by solving Equation 1for A when the left'hand side is put equal to zero.

In the particular casein which R1=R2=R; and C1=C2=C; 12:0; the values ofp and q-were and respectively. This gives an infinite zerophase-shiftfrequency for P=0; and the corresponding value of L is 0.4. It canbeseen from Equation 1 or 3 that the zero-phase-shift frequency for P=is given by 1/f= /2'.+rRC. For the special case in which R=1065 ohms 1?(ohms) 99 5,000 361 f(C./S.) 1,360 1, 6.5' 3,000

If in this case a compensating resistance Z3 for 11 be included in theseries arm in the manner explained with reference to Fig. 10, the valueof L for the network without n is now (from Equation 2 since A=0) so ,u.=2, and the value of Z3 should be 2r =708 ohms. The zero-phase.- shiftfrequency for P .-0 will however not be infinite, since an no longeraffects the frequency characteristic.

Two numerical examples will be given for the network of Fig. 4; in thefirst of which X1 and X2 are negative reactances represented bycondensers of capacities C1 and C2, and in the second of which K1 and X2are positive reactances represented by inductances L1 and L2.

The following measured values of the zerophase-shift frequency 1 wereobtained for various values of P:

The value of l= when rfvwi is about 480 ohms, so that smaller values ofP cannot be used.

Case 2 R1=1100 ohms 10:0.835 R2=1053 ohms q=0.030 L1=0.206 henry M=1.043

232:0.728 henry TlF-TO r2=120 ohms A final numerical; example of Fig. 7will be given:

R1 (resistance of 1'?) =2000 ohms R2 (resistance of 20)= 1000 ohms i C1(capacity of 19)=0.114 f.

Element I8 was short-circuited, so

The following measured values of the zerophase-shift frequency areobtained for various values of the capacity Cs of the condenser 23:

o en.) 0 691 Fig. 11. shows an oscillator circuit employing one of thenetworks according to the invention. The arrangement of Fig. 4 in whichthe reactances X1 and K2 are represented by inductances L1 and L2 isparticularly convenient for this purpose, and results in a very simplecir-' cuit. In Fig. 11 a thermionic valve 30 has a resistance 3|connected in series between the cathode and ground. The anode isconnected through a suitable anode resistance 32 to the positiveterminal 33 for the high tension supply source (not shown), the groundednegative terminal of which is. 3 3. The output oscillations may be takenfrom terminal 35 connected to the anode through a blocking condenser 36.

The cathode circuit of the valveis connected to the control grid circuitby a network according to the inventioncomprising a series arm includingan inductance coil 31 (L1) and a tapped resistance 38 (R1) and a shuntarm including an inductance coil. 39 (L2) and a tapped resistance i0(R2), a resistance 4| (r2) being shown connected in series with theinductance coil 39. It will be understood that the resistance 4|includes the resistance of the coil 39 and may not be represented by anyactual element.

The inductance coil 39 is also the primary winding of'a transformer, thesecondary winding 52 of which is connected to a high resistance potentiometer 43 and has one terminal connected to ground. The adjustablecontact of the potentiometer 43. is connected to the control grid of thevalve 3%. An adjustable resistance M (P) is connected between thetapping points on the resistances 38 and 4t.

'I'hetransformer formsd by the coils 39 and c2 mayhave a step-up ratioof the order of 3:1, and the potentiometer 43should have a very highresistance so that the inductance L2 is substantially the primaryinductance of the transformer.

Since there is substantially a zero phase change between the controlgrid and cathode of an amplifying valve arranged in the manner of Fig.11, oscillations will occur at the zero-phase-shift frequency of thecoupling network.

It will be clear, therefore, from what has been explained, that thenetwork may be designed to obtain any desired range of oscillationfrequencies by adjustment of the single resistance element 44; andmoreover, the amplitude of the oscillations may be made practicallyindependent of the frequency. The value of L for the network should bechosen suitably in relation to the transformer ratio and to the gain ofthe amplifier, and the potentiometer 43 provides a convenient fineadjustment for L to enable the oscillation condition to be correctlyset.

It will be understood that the output may be taken from the valve 30 invarious other ways. For example, a separate amplifying valve (not shown)may be provided, with its control grid (or cathode) connected directlyto the control grid (or cathode) of the valve 33. In this case theresistance 32 and condenser 36 will not be needed.

Attention is however drawn to the fact that the conditions for constantvoltage transfer ratio L are only approximately fulfilled in the circuitof Fig. 11 because of the presence of the resistance T2 in series withL2. The voltage applied to the control grid of the valve 30 shouldideally be proportioned to the voltage across the resistance 40, but itwill be seen that in Fig. 11, the voltage applied to the control grid isproportional to the voltage across L2, which is slightly different onaccount of the presence of m. However, if m is small, and/or the rangeof variation of the element 44 is small, the value of L will vary onlyslightly as this element is adjusted.

As already mentioned, the circuit of Fig. 11 provides a particularlysimple oscillation circuit. However, any of the other networks whichhave been described may be used to couple the cathode to the controlgrid of the value 3!}, with the bias and other operating arrangementsfor the valve modified where necessary, as will be understood by thoseskilled in the art. A step-up transformer will be required between theoutput of the network and the control grid, because the voltageamplification factor of the valve 30 arranged as a cathode follower isalways less than 1. Such a transformer should be designed to have a Veryhigh primary impedance otherwise an appreciable phase shift may beintroduced which might result in a corresponding small variation in thevoltage transfer ratio. It is however the particular advantage of thenetwork shown in Fig. 11 that the primary winding of this transformercan form an integral part of the network.

It will be understood also, that any of the networks according to theinvention may be used in the usual two-valve resistance reactanceoscillator circuits in which the anode of each valve is coupled to thecontrol grid of the other, one of the couplings including the networkwhich determines the frequency.

Owing to the fact that the oscillation amplitude can be independent ofthe frequency, an oscillator employing a network according to theinvention may be very easily used to produce frequency modulated waveswithout any accompanying amplitude modulation. Thus, for example, in anoscillation circuit employing any of the networks of Fig. 4, the element[6 need only be replaced by a carbon microphone, the resistance ofwhich, as is well known, varies in accordance with the pressure of thesound waves which impinge on the diaphragm. The. circuit being designedto generate a suitable carrier frequency, the output waves will befrequency modulated in accordance with the speech signals, without anyamplitude modulation.

It is, however, well known that the operation of a carbon microphone isnon-linear, since the resistance varies more rapidly for outwardexcursions of the diaphragm than for inward excursions. This elfect canbe very conveniently corrected by suitable choice of the resistance T1or T2 because as shown in Fig. 5 the steepness and shape of thecharacteristic curve relating the zero-phase-shift frequency to thevalue of P may be adjusted thereby until it is substantially the inverseof the corresponding microphone resistance characteristic.

Actually the two characteristic curves are not quite the same shape, butadequate compensation over a relatively wide frequency band is possible,so that practically undistorted frequency modulated waves will beobtained from the oscillator.

It may be pointed out that the variable resistance element may be usedfor a somewhat different purpose. Suppose a number of single frequencyoscillators according to Fig. 11 have to be manufactured. Then, as iswell known, the output frequency of the individual oscillators will varywithin a certain small range on account of the unavoidable manufacturingvariation of the elements which make up the circuit. By providing asingle adjustable resistance 44 connected to tapping points on theresistances 38 and 46 determined in the manner explained, the frequencyof each individual oscillator may be accurately set .ortrimmed by thesimple adjustment of the element 44, which may then be locked if desiredin any convenient manner. This forms a very inexpensive means ofobtaining an accurate output frequency in a circuit employing elementsmade to commercial limits. This method of trimming the network mayclearly be used whatever be the purpose for which the network is used.Networks such as these shown in Fig. 7 or 9 may be adjusted in the sameway by providing a small trimmin condenser for the element 23.

The variable element correspondin to 44 in Fig. 11 may be asemi-conducting device, such as a rectifier, which may be controlled byan adjustable voltage or current. Fig. 12 shows how the network of Fig-2 may be arranged, using a rectifier 45 connecting the tapping points inthe resistances 6 and 8. An additional resistance 46 is connected at oneend to the junction point of the elements 6 and i, and at the other endto a terminal 47. A direct current source of adjustable voltage (notshown) is intended to be connected with its positive terminal toterminal 41 and its negative terminal to terminal 4. As is well known,the effective resistance of the rectifier 45 will depend on the appliedvoltage, the adjustment of Which will change the zero-phaseshiftfrequency accordingly. This provides a convenient means of remotecontrol of the network. If the network be used as part of an oscillatorcircuit similar to that shown in Fig. 11 for eX ample, the oscillationfrequency may be conveniently controlled in this way. If the sourceconnected to terminals 4 and 41 includes a source of signal voltage, thearrangement provides an alternative means of frequency modulation of theoscillations. If the rectifier 45 is reversed, then the connections atterminals 4 and 4! to the direct current source should also be reversed.

Fig. 13 shows a variation of Fig. 12 in which a bridge rectifier 48 isused instead of the single rectifier 45. In this case an extraresistance corresponding to 46 is not needed. One pair of diagonalterminals of the bridge rectifier are respectively connected to the tapson the resistances 6 and 8, and the other pair to two terminals 49 and59, to which a direct current source (not shown) should be connected.This source may include a source of modulating signal voltage when thenetwork is used in an oscillator circuit, as in the case of Fig. 12.

Another convenient method of controlling the zero-phase-shift frequencyof a network such as any of those covered by Fig. 4 is to replace theresistance IE, or part of it, by the resistance element of an indirectlyheated thermistor, the heating coil of which is connected to a source ofadjustable direct or alternating current.

It will be evident that any of the networks covered by Fig. 4 may beprovided with a rectifier arranged as in Fig. 12 or 13, and any suchnetworks may be used in oscillator circuits similar to that shown inFig. 11, or in any other manner.

What is claimed is:

1. A phase shift network of the L-type havin a series and a shunt arm;the series arm comprising a capacitor and a resistor connected thereto,the shunt arm comprising a capacitor, and a resistor in paralleltherewith; means for controlling the frequency at which the networkprovides zero phase shift consisting essentially of an additionalresistor having one terminal connected to an intermediate point of saidseries arm resistor and the other terminal connecting to an intermediatepoint of said shunt arm resistor.

2. A phase shifting network of the L -type having a series and a shuntarm; each of said arms comprising a resistor and a reactive memberconnected thereto; means for controlling the frequency at which thenetwork provides zero phase shift consisting essentially of an impedancemember having one terminal connected to an intermediate point of amember in said series arm and the other terminal connected to anintermediate point of a member in said shunt arm, said impedance memberand said members to which it is connected presenting the same typeimpedance.

T 3. A phase shifting network of the L.type having a series arm and ashunt arm; each of said arms comprising a resistor and a reactive memberconnected thereto; means for controlling the frequency at which thenetwork provides zero phase shift consisting essentially of a reactancemember having one terminal connected to an intermediate point of areactive member in said series arm and the other terminal connected toan intermediate point of a reactive member in said shunt arm, saidreactance member and said reactive members to which it is connectedpresenting the same type reactance.

4. A phase shifting network according to claim 2f ,wherein the membersin each of said arms comprise a delta formation, and said impedancemember is connected between the apices of the deltas.

"5 A phase shifting network according to claim 2 wherein the impedancemember is a rectifier and the members to which the impedance memher isconnected are resistors.

6. A phase shiftin network according to claim 3 in which said reactancemember and said reactive members to which the reactance member isconnected are capacitors.

EDMUND RAMSAY WIGAN.

REFERENCES CITED The following references are of record in the file ofthis patent:

UNITED STATES PATENTS Number Name Date 1,442,781 Nichols Jan. 16, 19232,043,345 Bobis June 9, 1936 2,072,946 Farnham Mar. 9, 1937 --2,093,665Tellegen Sept. 21, 1937 2,173,427 Scott Sept. 19, 1939 2,236,985Bartelink Apr. 1, 1941 2,294,863 Hadfield Sept. 1, 1942 2,298,177 ScottOct. 6, 1942 2,300,632 Poch Nov. 3, 1942 1 2,418,842 Kinsburg Apr. 15,1947 FOREIGN PATENTS Number Country Date 839,492 France Jan. 4, 1939

